The concept of detrimental reliance is typical of common law systems. "Confiança prejudicial" is a literal translation. Depending on the context, further explanation may be necessary, such as "quebra de confiança por uma das partes do contrato, gerando prejuízos para a outra" or "prejuízo gerado por descumprimento de promessas feitas no âmbito de um contrato".
when one party depends on or trusts another party and this causes the first party to be in a worse position
The trial judge found in favour of Smith, finding that Watson had failed to prove detrimental reliance.